Amazon has unveiled its ambitious music streaming service, Cloud Player, which allows users to play songs across a number of computers and Android smartphones.

Music lovers will be able to upload most of their existing music library – including tracks bought through Apple's iTunes – to Amazon, as well as buy new songs for digital playback.

The online retailer has stolen a march on rivals Apple and Google with the service, known as Amazon Cloud Player, with both internet giants planning their own forays into music streaming. The move also represents Amazon's repositioning as an entertainment destination, rather than just an online marketplace.

Another element of the service, Amazon Cloud Drive, works like a "digital music locker" where users can upload thousands of songs and listen to them via Cloud Player on any computer or Android smartphone.

"Our customers have told us they don't want to download music to their work computers or phones because they find it hard to move music around to different devices," said the Amazon vice-president of music and movies, Bill Carr. "Now, whether at work, home, or on the go, customers can buy music from Amazon MP3, store it in the cloud and play it anywhere."

As an introductory offer, Cloud Player is free to Amazon account holders, although users can pay to increase the amount of music able to be stored on Cloud Drive. Customers start with 5GB of storage space – equivalent to just over 1,000 songs – and those who buy an MP3 album from the Amazon store will be upgraded to the larger 20GB service.

Apple and Google are said to be planning similar ventures, while Sony's Music Unlimited also offers a digital music locker, but charges upwards of £4 a month. Agreements with all four major record labels are thought to be the sticking point for Apple's and Google's streaming services, with rights owners apparently unhappy with the idea of a one-off payment each time a track is played on any device.

Beyond Oblivion, an online music site partly owned by Rupert Murdoch's News Corporation, is proposing to woo rights holders by paying them a royalty each time their music is played. The service, which secured $77m (£47m) on investment earlier this month, is yet to launch and negotiations with music labels said to be at a "very advanced stage".

Amazon said it has sidestepped legal uncertainties about allowing users to upload music from their computer – some of which may have been downloaded illegally – by being the equivalent of any other storage device, such as an external hard drive.

The Amazon director of music, Craig Pape, said: "We don't need a licence to store music. The functionality is the same as an external hard drive."

• Amazon's online retail rival eBay yesterday stepped up its attempt to become the primary destination for internet shopping by buying GSI Commerce, an online services firm, for $2.4bn. The acquisition will allow eBay to expand beyond its network of small retailers into the larger retail market.